WASHINGTON (Reuters) - Republican presidential candidate Donald Trump on Friday abandoned his false claim that Barack Obama was not born in the United States after spending five years peddling conspiracy theories that the country's first African-American president started life as a foreigner.

But, never one to let a controversy go without fanning its flames, Trump accused Hillary Clinton, his Democratic rival in the Nov. 8 election, of starting the so-called birther movement in her failed 2008 presidential campaign against Obama, a claim that does not stand up to scrutiny.

Trump, who has won back some ground in opinion polls and made the White House race more competitive after he went through a summer slump, made his announcement in an attempt to clear the air as he prepares for the first of three televised presidential debates with Clinton on Sept. 26.

"President Barack Obama was born in the United States. Period," said Trump, a real estate developer. "Now we all want to get back to making America strong and great again," he said at an event in Washington at a new Trump International Hotel down the street from the White House.

Devoting only about 30 seconds to the subject, Trump did not apologize and did not expand upon his abrupt decision to shift from a stance he held for five years.

The New York businessman brought up the birther controversy as far back as 2011, appealing to a right-wing fringe of voters who formed the early base of his support when he launched his presidential bid last year.

The birther conspiracy movement is aimed at challenging the legality of Obama's presidency - the U.S Constitution requires that a president be a natural-born citizen.

During his presidential campaign, Trump has readily trafficked in other theories that are the stuff of American supermarket tabloids.

There was his declaration that the father of U.S. Senator Ted Cruz, one of Trump's many rivals for the Republican nomination, might have been linked to the assassin of President John F. Kennedy. And there was his false claim that thousands of Muslims in Jersey City, New Jersey, cheered when the World Trade Center twin towers collapsed in the Sept. 11, 2001, attacks.

In making his announcement on Friday, Trump advanced a widely debunked claim that Clinton and her 2008 campaign had been the original birthers.

"Hillary Clinton and her campaign of 2008 started the birther controversy. I finished it. You know what I mean," he said.

His campaign directed reporters to a 2007 memo from then-Clinton adviser Mark Penn, who had encouraged the Clinton campaign to go negative against Obama by saying that his Hawaiian birth and boyhood in Indonesia gave him limited roots in American values and culture.

Penn eventually left the Clinton campaign, and his advice was never acted upon.

"A NEW LIE"

The Democratic National Committee on Friday condemned Trump's bid to link Clinton to the birther idea. "He had the audacity to spout a new lie about the birther movement that he helped to build," it said.

Clinton, who leads Trump by 4 percentage points in the latest Reuters/Ipsos poll, on Friday demanded Trump apologize to the president for having helped spread the birther idea and said Trump had tried to "delegitimize our first black president."

"His campaign was founded on this outrageous lie. There is no erasing it in history," Clinton said in an address to the Black Women's Association in Washington.

Clinton seized on the issue after struggling to overcome the fallout from her remark a week ago that half of Trump's supporters are in a "basket of deplorables" and her initial secrecy about her pneumonia diagnosis.

Obama, who produced the longer version of his Hawaiian birth certificate in 2011 to prove doubters wrong, had famously mocked Trump over the issue at a White House Correspondents Association dinner as the wealthy businessman sat in the audience fuming.

Still, Trump clung to the contention that Obama was foreign-born, tweeting in August 2012: "An 'extremely credible source' has called my office and told me that @BarackObama's birth certificate is a fraud."

On Friday, Obama was asked for his reaction to the latest Trump declaration.

"I'm shocked that a question like that has come up at a time when we have so many other things to do. Well, I'm not that shocked actually. It's fairly typical. We've got other things to attend to," he said. "I was pretty confident about where I was born."

Trump's embrace of the birther movement has incensed black Americans, whose votes Trump has been trying to court.

Members of the Congressional Black Caucus held a news conference on Friday to urge African-American voters to resist any temptation to support Trump.

"I'm wondering when this country is going to awaken from this reality show," said Representative Brenda Lawrence, a Democrat.

First lady Michelle Obama told a crowd in Fairfax, Virginia, that her husband has set a strong example for those who have doubted "whether my husband was even born in this country."

"Well, during his time in office, I think Barack has answered those questions with the example he's set: by going high when they go low. And he’s answered these questions with the progress that we’ve achieved together," she said.

At a rally in Miami later on Friday, Trump pushed back on the idea that he and his supporters were racist, saying that when Democrats are in trouble politically, "they always pull out the racist word."

He walked out at the rally to a song from the musical "Les Miserables" in front of a backdrop that read "Les Deplorables," a reference to Clinton's comment last week about his supporters.

The issue of Obama's birthplace has not been a factor in the campaign leading up to the November presidential election, but it resurfaced in recent days, taking the focus of Trump's White House bid away from topics such as immigration, trade and the economy, which he has been using to hit Clinton.

Trump revived the birther controversy on Thursday in an interview with The Washington Post when he declined to say whether he believed Obama was born in Hawaii.

Trump had promised "a big announcement" about the birther issue on Friday, giving the impression it was the purpose of the event at his hotel.

Instead, he held off saying anything about it through more than 20 minutes of endorsements from military veterans. Only then did Trump make a brief statement about Obama's birth.

Trump devoted more time at the beginning of the event to talking about his hotel where the event took place. He ignored reporters' shouted questions.